# hw1 - BIOMETRICS CSE190 Fall 2006 Assignment 1 Due 1 For a...

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Unformatted text preview: BIOMETRICS CSE190 Fall 2006 Assignment 1 Due: October 19, 2006 1. For a single feature, what are the optimal decision regions where: • Ω = { ω 1 , ω 2 } • P(x | ω 1 ) = N(2, 0.5) (Normal distribution) • P(x | ω 2 ) = N(1.5, 0.2) • P( ω 1 ) = 2/3 • P( ω 2 ) = 1/3 • λ 11 = 0, λ 12 = 1, λ 21 = 1, λ 22 =0 2. Select the optimal decision regions for the above problem when: • λ 11 = 1, λ 12 = 2, λ 21 = 3, λ 22 =4 3 . Problem 2.13 in DHS. In many pattern classification problems one has the option either to assign the pattern to one of c classes, or to reject it as being unrecognizable. If the cost for rejects is not too high, rejection may be a desirable action. Let ⎪ ⎩ ⎪ ⎨ ⎧ + = = = = Otherwise c i c j i j i s r j i λ λ ω α λ 1 ,..., 1 , , ) | ( Where λ r is the loss incurred for chosing the (c+1)th action, rejection, and λ s is the loss incurred for making any substitution error. Show that the minimum risk is obtained if we decide ω i if P ( ω i...
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hw1 - BIOMETRICS CSE190 Fall 2006 Assignment 1 Due 1 For a...

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